Introduction: Canonical search-and-matching models determine wages by imposing fixed Nash weights that are interpreted as bargaining power and treated as exogeneous. I propose a tractable model in which workers and firms may keep prospecting for alternative matches while they negotiate. The key mechanism is straightforward: a party exits the current match only if its previous offer was rejected and it subsequently meets a new potential partner. I impose this rule in a benchmark set-up and later endogenise it in the full model. This feature, first imposed and later endogenised, generates surplus shares that move with market tightness and, to my knowledge, is the first bargaining model in matching markets that does so.

Methods: The model embeds Rubinstein bargaining in a matching market with tightness θ, defined as the ratio of vacancies over unemployed. Workers find jobs at rate p(θ) (strictly increasing), while firms fill vacancies at rate q(θ) (strictly decreasing). In the benchmark variant the firm proposes first and a proposer does not search within the same period; these restrictions deliver closed-form solutions that make the mechanism transparent. All assumptions are relaxed in the full game.

Results: The ratio of worker surplus over firm surplus is given by

β(θ)= (1−q(θ))/(2−q(θ))​

so the worker’s surplus share grows monotonically in θ. Intuitively, a tighter market raises the probability the worker can answer with a counter-offer before being deserted, increasing the bargaining power. When move order and exit decisions are endogenised, a unique subgame-perfect equilibrium survives and the positive sign of ∂β/∂θ >0 persists under reasonable parameter values.

Conclusions: By linking surplus division directly to market tightness, the protocol results in a tractable, game-theoretic foundation for variable and asymmetric bargaining power inside matching markets and opens new ground for analysing wage dynamics and other two-sided negotiations.